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Morten Hjorth-Jensen
2023-11-16 06:33:54 +01:00
parent 73e82cd8dd
commit 2c1f27b519
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@@ -42,14 +42,6 @@ doconce format html week46.do.txt --html_style=bootstrap --pygments_html_style=d
None,
'decision-trees-overarching-aims'),
('Basics of a tree', 2, None, 'basics-of-a-tree'),
('A Sketch of a Tree, Regression problem',
2,
None,
'a-sketch-of-a-tree-regression-problem'),
('A Sketch of a Tree, Classification problem',
2,
None,
'a-sketch-of-a-tree-classification-problem'),
('A typical Decision Tree with its pertinent Jargon, '
'Classification Problem',
2,
@@ -257,67 +249,65 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._week46-bs001.html#plan-for-week-46" style="font-size: 80%;">Plan for week 46</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs002.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs003.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs004.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs005.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs006.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs007.html#general-features" style="font-size: 80%;">General Features</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs008.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
<!-- navigation toc: --> <li><a href="#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs010.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs011.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs012.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs013.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs014.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs015.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs016.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs017.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs018.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs019.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs020.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs021.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs023.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs024.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs025.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs026.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs027.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs028.html#the-table" style="font-size: 80%;">The Table</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs029.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs030.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs031.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs032.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs033.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs034.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs035.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs036.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs037.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs038.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs039.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs040.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs041.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs042.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs043.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs044.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs045.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs046.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs047.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs048.html#bagging" style="font-size: 80%;">Bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs049.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs050.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs051.html#random-forests" style="font-size: 80%;">Random forests</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs052.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs053.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs054.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs055.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs056.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs057.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs058.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs059.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs060.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs061.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs062.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs063.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs064.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs004.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs005.html#general-features" style="font-size: 80%;">General Features</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs006.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs007.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs008.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
<!-- navigation toc: --> <li><a href="#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs010.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs011.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs012.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs013.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs014.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs015.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs016.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs017.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs018.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs019.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs020.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs021.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs023.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs024.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs025.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs026.html#the-table" style="font-size: 80%;">The Table</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs027.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs028.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs029.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs030.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs031.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs032.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs033.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs034.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs035.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs036.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs037.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs038.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs039.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs040.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs041.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs042.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs043.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs044.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs045.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs046.html#bagging" style="font-size: 80%;">Bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs047.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs048.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs049.html#random-forests" style="font-size: 80%;">Random forests</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs050.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs051.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs052.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs053.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs054.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs055.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs056.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs057.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs058.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs059.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs060.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs061.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs062.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
</ul>
</li>
@@ -329,117 +319,21 @@ MathJax.Hub.Config({
<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
<a name="part0009"></a>
<!-- !split -->
<h2 id="decision-trees-and-regression" class="anchor">Decision trees and Regression </h2>
<h2 id="a-top-down-approach-recursive-binary-splitting" class="anchor">A top-down approach, recursive binary splitting </h2>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="inner_cell">
<div class="input_area">
<div class="highlight" style="background: #f8f8f8">
<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> PolynomialFeatures
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression
steps<span style="color: #666666">=250</span>
distance<span style="color: #666666">=0</span>
x<span style="color: #666666">=0</span>
distance_list<span style="color: #666666">=</span>[]
steps_list<span style="color: #666666">=</span>[]
<span style="color: #008000; font-weight: bold">while</span> x<span style="color: #666666">&lt;</span>steps:
distance<span style="color: #666666">+=</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(<span style="color: #666666">-1</span>,<span style="color: #666666">2</span>)
distance_list<span style="color: #666666">.</span>append(distance)
x<span style="color: #666666">+=1</span>
steps_list<span style="color: #666666">.</span>append(x)
plt<span style="color: #666666">.</span>plot(steps_list,distance_list, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;green&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;Random Walk Data&quot;</span>)
steps_list<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(steps_list)
distance_list<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(distance_list)
X<span style="color: #666666">=</span>steps_list[:,np<span style="color: #666666">.</span>newaxis]
<span style="color: #408080; font-style: italic">#Polynomial fits</span>
<span style="color: #408080; font-style: italic">#Degree 2</span>
poly_features<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=2</span>, include_bias<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)
X_poly<span style="color: #666666">=</span>poly_features<span style="color: #666666">.</span>fit_transform(X)
lin_reg<span style="color: #666666">=</span>LinearRegression()
poly_fit<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>fit(X_poly,distance_list)
b<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>coef_
c<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>intercept_
<span style="color: #008000">print</span> (<span style="color: #BA2121">&quot;2nd degree coefficients:&quot;</span>)
<span style="color: #008000">print</span> (<span style="color: #BA2121">&quot;zero power: &quot;</span>,c)
<span style="color: #008000">print</span> (<span style="color: #BA2121">&quot;first power: &quot;</span>, b[<span style="color: #666666">0</span>])
<span style="color: #008000">print</span> (<span style="color: #BA2121">&quot;second power: &quot;</span>,b[<span style="color: #666666">1</span>])
z <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0</span>, steps, <span style="color: #666666">.01</span>)
z_mod<span style="color: #666666">=</span>b[<span style="color: #666666">1</span>]<span style="color: #666666">*</span>z<span style="color: #666666">**2+</span>b[<span style="color: #666666">0</span>]<span style="color: #666666">*</span>z<span style="color: #666666">+</span>c
fit_mod<span style="color: #666666">=</span>b[<span style="color: #666666">1</span>]<span style="color: #666666">*</span>X<span style="color: #666666">**2+</span>b[<span style="color: #666666">0</span>]<span style="color: #666666">*</span>X<span style="color: #666666">+</span>c
plt<span style="color: #666666">.</span>plot(z, z_mod, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;r&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;2nd Degree Fit&quot;</span>)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;Polynomial Regression&quot;</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&quot;Steps&quot;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&quot;Distance&quot;</span>)
<span style="color: #408080; font-style: italic">#Degree 10</span>
poly_features10<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=10</span>, include_bias<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)
X_poly10<span style="color: #666666">=</span>poly_features10<span style="color: #666666">.</span>fit_transform(X)
poly_fit10<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>fit(X_poly10,distance_list)
y_plot<span style="color: #666666">=</span>poly_fit10<span style="color: #666666">.</span>predict(X_poly10)
plt<span style="color: #666666">.</span>plot(X, y_plot, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;black&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;10th Degree Fit&quot;</span>)
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
<span style="color: #408080; font-style: italic">#Decision Tree Regression</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeRegressor
regr_1<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>)
regr_2<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=5</span>)
regr_3<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=7</span>)
regr_1<span style="color: #666666">.</span>fit(X, distance_list)
regr_2<span style="color: #666666">.</span>fit(X, distance_list)
regr_3<span style="color: #666666">.</span>fit(X, distance_list)
X_test <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0.0</span>, steps, <span style="color: #666666">0.01</span>)[:, np<span style="color: #666666">.</span>newaxis]
y_1 <span style="color: #666666">=</span> regr_1<span style="color: #666666">.</span>predict(X_test)
y_2 <span style="color: #666666">=</span> regr_2<span style="color: #666666">.</span>predict(X_test)
y_3<span style="color: #666666">=</span>regr_3<span style="color: #666666">.</span>predict(X_test)
<span style="color: #408080; font-style: italic"># Plot the results</span>
plt<span style="color: #666666">.</span>figure()
plt<span style="color: #666666">.</span>scatter(X, distance_list, s<span style="color: #666666">=2.5</span>, c<span style="color: #666666">=</span><span style="color: #BA2121">&quot;black&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;data&quot;</span>)
plt<span style="color: #666666">.</span>plot(X_test, y_1, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;red&quot;</span>,
label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=2&quot;</span>, linewidth<span style="color: #666666">=2</span>)
plt<span style="color: #666666">.</span>plot(X_test, y_2, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;green&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=5&quot;</span>, linewidth<span style="color: #666666">=2</span>)
plt<span style="color: #666666">.</span>plot(X_test, y_3, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;m&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=7&quot;</span>, linewidth<span style="color: #666666">=2</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&quot;Data&quot;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&quot;Darget&quot;</span>)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;Decision Tree Regression&quot;</span>)
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
</pre>
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<p>Unfortunately, it is computationally infeasible to consider every
possible partition of the feature space into \( J \) boxes. The common
strategy is to take a top-down approach
</p>
<p>The approach is top-down because it begins at the top of the tree (all
observations belong to a single region) and then successively splits
the predictor space; each split is indicated via two new branches
further down on the tree. It is greedy because at each step of the
tree-building process, the best split is made at that particular step,
rather than looking ahead and picking a split that will lead to a
better tree in some future step.
</p>
<p>
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